canonicalThreshold
plain-language theorem explainer
The canonical materials threshold is the real constant φ − 3/2. Anyone comparing domain costs or Mott-scale cutoffs inside RS materials module 10 cites this value. It is a one-line definitional constant, not a proved inequality.
Claim. Define the canonical threshold by $T_{\mathrm{can}} := \varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of Recognition self-similarity.
background
Materials RS Module 10 treats the Mott transition ratio $U/t$. The module records a structural match of $\varphi^3 \approx 4.24$ against the experimental window 3–5, with status STRUCTURAL THEOREM (0 sorry, 0 axiom).
The constant $\varphi$ is imported from Recognition Constants: it is the unique positive self-similar fixed point forced at T6 of the unified forcing chain. Cost primitives (J-cost and related domain costs) come from the Cost import; siblings on this file evaluate a domain cost, prove it nonnegative, and certify the module.
This declaration simply names the real scale $\varphi - 3/2$ used as the local cutoff beside those cost lemmas.
proof idea
Definitional only. The body is the real arithmetic expression $\varphi - 3/2$; there is no tactic proof and no lemma application.
why it matters
Anchors the numeric cutoff for the materials certificate layer (RSMatl010Cert and the inhabited cert on the same module). The parent module’s claim is the Mott $U/t$ structural match at $\varphi^3$ in the band 3–5. In the broader RS stack, $\varphi$ is the T6 fixed point; thresholds built from $\varphi$ keep materials comparisons in the same native units as the mass ladder and the eight-tick octave. The definition itself does not close the Mott match; it supplies the scale those certificates compare against.
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